The BBC has been asked to clarify if any efforts are made to “deliberately invite or attract” members of far-right groups to the audience of its flagship political programme, Question Time.

Baroness Warsi and Labour MP Debbie Abrahams have written to the BBC’s director general Tony Hall, asking him to consider also introducing a new code of conduct for panelists and the audience, and to stop sharing inflammatory videos from the show on social media.

It follows the BBC’s decision last month to upload on Twitter comments made by one recent audience member who claimed migrants “were flooding in” to the UK and costing public services too much.

Later, the individual was alleged to have stood in a general election for the neo-nazi National Front and be an active a supporter of the far right figurehead, Tommy Robinson, founder of the Islamophobic English Defence League.

Warsi and Abrahams, co-chairs of the new all-party group Compassion in Politics, argue that the BBC has a duty to avoid inflaming hate. Their letter asks how the Question Time audience is sourced and seeks a response to their assertion that far right supporters are invited to appear on the show.

The letter says: “We understand the producers of the show seek out ‘controversial members of the audience – including those of far-right campaign groups – in an attempt to curry large ratings.”

BBC sources, however, strongly rejected the claim they sought “audiences from any extremist groups to curry ratings”.

Recently the Question Time presenter, Fiona Bruce, described the “level of toxicity” on the show and admitted she had not anticipated how angry the show’s audiences would be.

Warsi and Abrahams write: “By providing a platform for views that are racist or sexist, the institution is normalising them and contributing to the coarsening of public debate and the growing toxicity of our politics.

By providing a platform for views that are racist or sexist, the institution is normalising them and contributing to the coarsening of public debate and the growing toxicity of our politics.

“We therefore invite the BBC to let us know what steps it will now be taking to ensure that the recent controversies surrounding Question Time are not repeated.”

A BBC spokesperson said: “We take the issues raised in this letter very seriously and regularly discuss the tone and content of the programme, and constantly review how we engage with people on social media. Question Time is an important part of the schedule, as one of the few programmes which allows audiences to hold to account those in power.”

The calls for greater efforts to prevent racist views being aired on Question Time arrive during an otherwise positive period for the BBC as the virus outbreak has swiftly underscored its national status.

Ten million viewers watched the prime minister’s press conference on Wednesday. The corporation has stepped up to its dormant “civil contingency” role by making changes to schedules, even where not forced to do so by social isolation advice. The One Show is now partly given over to updates and information, while a new health show has been put together at speed. Newsround and the rest of the CBBC children’s programming line-up has also shifted to provide increased entertainment and information.

Last week ratings for BBC TV news reflected the highest figures for a decade for conventional bulletins.

A survey conducted by Havas Media Group found the BBC was regarded as the most reliable brand during the crisis for 64% of the 1,500 people surveyed.

After surveying nearly 1,500 respondents, the Covid-19 Media Behaviours Report, found that more than half of the public are turning to BBC news channels and stations more than before the pandemic hit Britain. The researchers also found that more people are watching more television as well as increasing their use of social media sites.

All news brands are seeing a big upward curve, with more than a third of people saying they are reaching for print and online newspaper coverage more often.

A separate study found that the Observer and Guardian were the most trusted print and digital news brands among publishers, and more than 80% of readers now say they most trust the shared online site, visited by more than 24 million unique users on several days last week.

• This article was amended on 23 March 2020 to correct the reliability rating of the BBC to 64%, not 61% as an earlier version stated. It was further amended to make clear that the survey from which this finding came was the Covid-19 Media Behaviours Report.